The newspaper reported that Peralta will receive $6 million over the two seasons with a $2.5 million option for the 2015 season. The contract is subject to the right-handed pitcher passing a physical.
"Some teams offered a little bit more money, but I got what I thought I was worth and I was happy with it," Peralta told the newspaper from the Dominican Republic. "I didn't want to go anywhere else."
Peralta, who turns 37 in March, made 76 appearances last season, posting a 2-6 record with two saves and a 3.63 ERA. He was credited with 37 holds.
Peralta joins closer Fernando Rodney as members of the Rays bullpen who could have been pitching elsewhere next season but will stay with Tampa Bay.
Rodney, the American League's comeback player of the year, set a club record with a career-best 48 saves in his first season with the Rays. The 35-year-old right-hander had a 0.60 ERA, a big league record for a reliever with at least 50 innings pitched. Tampa Bay picked up his $2.5 million option rather than paying him a $250,000 buyout.
The Tampa Bay Times reported that the Rays also are interested in re-signing two other members of their bullpen, left-hander J.P. Howell and right-hander Kyle Farnsworth, with talks planned with both pitchers.
Information from The Associated Press was used in this report.